Остання редакція: 12-05-2020

#### Тези доповіді

The interpretation of the concept of probability, as the degree of possibility of realization of a corresponding event, at the turn of the XIX and XX centuries against the background of achievements in the field of physics (mainly quantum physics) became relevant not only among mathematicians and specialists, who in their professional activity are faced with the need to predict certain or other events, but also within the philosophical community, which in turn led to the development of the interpretation of probability as a certain philosophical category. Studies of this category, which have coincided with a heightened interest in multifaceted (not binary) logic, have led to the emergence of appropriate integrated structures that rely on the concepts of both logic and probability.

The essence of mutual penetration (for today it is possible, even, to speak of a definite merger) concepts of logic and probability and the consequences of this process can be understood only in the framework of the relevant historical discourse.

It is believed that logic originated in the IV century BC. in ancient Greece and was associated with oratory. Together, logic and rhetoric reflected the processes of mastering the basics of argumentation, logical rules of proof, rules for the formation of forms of thinking. It took a long time before the works of F. Bacon, R. Descartes, G. Leibniz logic (as a science) was directed to form conclusions on the basis of judgments. English scientist F. Bacon, the founder of inductive logic, one of the first in his research turned to experiment. A universal method of inquiry, he declared the movement of thought from individual facts to summarizing conclusions. French philosopher R. Descartes was (on the contrary) a supporter of deductive logic, which aims to establish the truth of specific facts on the basis of general conclusions. German philosopher G. Leibniz first expressed the need for the creation of symbolic or mathematical logic. However, Leibniz's idea of the possibility, necessity, and productivity of summarizing judgments to appropriate calculations has not been found in many years by either philosophers or mathematicians. Symbolic logic really began to be created only in the middle of the nineteenth century, by the activities of J. Bull, De Morgan, C. Pierce and others. The application of methods of symbolic logic to solving problems that arose in formal logic allowed us not only to solve these problems, but also to formulate and largely solve problems that could not even be posed within formal logic. This, of course, triggered a revolutionary shift in the early twentieth century, both in formal logic and in all scientific fields that are in one way or another related to it. Modern formal logic is often equated with mathematical logic. However, this judgment cannot be accepted in its entirety. Mathematically in the strict sense, we can only recognize the part of formal logic that is connected with the study of mathematical artifacts. At the same time, modern logic contains many sections and branches that operate in other concepts, refer more to philosophy than to mathematics (modal logic, inductive logic, multi-valued logic, logic of norms and estimates, etc.), and hence apply verbal presentation of hypotheses and conclusions.

Interpretation of Probability as a Degree of Reasonable Faith, which was proposed in the 1920s by English scientist J.M. Keynes is considered to be the first interpretation that has largely contributed to the founding of structures where the concepts of probability and logic converge. Analyzing and criticizing both classical and frequency interpretations of probability, J. Keynes suggested to consider probability as a degree of reasonable faith, ascribed to appropriate statements (events) with precisely fixed data. In Keynes's interpretation, probability (as some numerical value) is set for the logical relationship between two sets of statements. It reflects the degree of belief in the correctness (or incorrectness) of expression, and the numerical value of this degree of faith is not constant, and varies depending on the available knowledge (information available) about the analyzed phenomena, objects, processes. All of the above points to the analytical rather than the empirical nature of probability. Keynes himself emphasized the objective nature of his interpretation of probability. Although the degree of reasonable faith (probability) varies with the change in available knowledge, it characterizes the relationship between objects that is independent of human consciousness. "As important as logic is the category," argued Keynes, "probability is not subjective. It is not a matter of human whim. The statement is probably not because we think about it. As soon as the facts which determine our knowledge are provided, in such circumstances what is considered probable and what is improbable is fixed objectively and does not depend on the opinion of the subject. Probability theory is logical because it deals with a degree of faith that is reasonable in the circumstances, and not simply with an actual belief that can be both reasonable and not reasonable. "

Attempts to construct a rigorous system (theory) of probabilistic logic on the basis of the above conclusions have failed. What was done in this direction was too cumbersome and inconvenient. The ideas described in practical activity have not been widely used. At the same time, it should be noted that the works in this direction were not in vain. They fostered an awareness of the link between logic and probability, which eventually led to the emergence of new practically useful areas of science, including integrated logic-probabilistic and probabilistic-logical structures, which are nowadays increasingly used in various fields of activity.